Computational aerodynamics of low Reynolds number plunging,pitching and flexible wings for MAV applications

Micro air vehicles （MAV＇s） have the potential to revolutionize our sensing and information gathering capabilities in environmental monitoring and homeland security areas. Due to the MAV＇s＇ small size, flight regime, and modes of operation, significant scientific advancement will be needed to create this revolutionary capability. Aerodynamics, structural dynamics, and flight dynamics of natural flyers intersects with some of the richest problems in MAV＇s, inclu- ding massively unsteady three-dimensional separation, transition in boundary layers and shear layers, vortical flows and bluff body flows, unsteady flight environment, aeroelasticity, and nonlinear and adaptive control are just a few examples. A challenge is that the scaling of both fluid dynamics and structural dynamics between smaller natural flyer and practical flying hardware/lab experiment （larger dimension） is fundamentally difficult. In this paper, we offer an overview of the challenges and issues, along with sample results illustrating some of the efforts made from a computational modeling angle.

A STUDY ON THE MECHANISM OF HIGH-LIFT GENERATION BY AN AIRFOIL IN UNSTEADY MOTION AT LOW REYNOLDS NUMBER

The aerodynamic force and flow structure of NACA 0012 airfoil performing an unsteady motion at low Reynolds number (Re = 100) are calculated by solving Navier-Stokes equations. The motion consists of three parts: the first translation, rotation and the second translation in the direction opposite to the first. The rotation and the second translation in this motion are expected to represent the rotation and translation of the wing-section of a hovering insect. The flow structure is used in combination with the theory of vorticity dynamics to explain the generation of unsteady aerodynamic force in the motion. During the rotation, due to the creation of strong vortices in short time, large aerodynamic force is produced and the force is almost normal to the airfoil chord. During the second translation, large lift coefficient can be maintained for certain time period and (C) over bar (L), the lift coefficient averaged over four chord lengths of travel, is larger than 2 (the corresponding steady-state lift coefficient is only 0.9). The large lift coefficient is due to two effects. The first is the delayed shedding of the stall vortex. The second is that the vortices created during the airfoil rotation and in the near wake left by previous translation form a short 'vortex street' in front of the airfoil and the 'vortex street' induces a 'wind'; against this 'wind' the airfoil translates, increasing its relative speed. The above results provide insights to the understanding of the mechanism of high-lift generation by a hovering insect.

Effect of Spanwise Flexibility on Propulsion Performance of a Flapping Hydrofoil at Low Reynolds Number

Spanwise flexibility is a key factor influencing propulsion performance of pectoral foils. Performances of bionic fish with oscillating pectoral foils can be enhanced by properly selecting the spanwise flexibility. The influence law of spanwise flexibility on thrust generation and propulsion efficiency of a rectangular hydro-foil is discussed. Series foils constructed by the two-component silicon rubber are developed. NACA0015 shape of chordwise cross-section is employed. The foils are strengthened by fin rays of different rigidity to realize variant spanwise rigidity and almost the same chordwise flexibility. Experiments on a towing platform developed are carried out at low Reynolds numbers of 10 000, 15 000, and 20 000 and Strouhal numbers from 0.1 to 1. The following experimental results are achieved: (1) The average forward thrust increases with the St number increased; (2) Certain degree of spanwise flexibility is beneficial to the forward thrust generation, but the thrust gap is not large for the fins of different spanwise rigidity; (3) The fin of the maximal spanwise flexibility owns the highest propulsion efficiency; (4) Effect of the Reynolds number on the propulsion efficiency is significant. The experimental results can be utilized as a reference in deciding the spanwise flexibility of bionic pectoral fins in designing of robotic fish prototype propelled by flapping-wing.

A new bionic MAV's flapping motion based on fruit fly hovering at low Reynolds number

On the basis of the studies on the high unsteady aerodynamic mechanisms of the fruit fly hovering the aerodynamic advantages and disadvantages of the fruit fly flapping motion were analyzed. A new bionic flapping motion was proposed to weaken the disadvantages and maintain the advantages, it may be used in the designing and manufacturing of the micro air vehicles （MAV＇s）. The translation of the new bionic flapping motion is the same as that of fruit fly flapping motion. However, the rotation of the new bionic flapping motion is different. It is not a pitching-up rotation as the fruit fly flapping motion, but a pitching-down rota- tion at the beginning and the end of a stroke. The numerical method of 3rd-order Roe scheme developed by Rogers was used to study these questions. The correctness of the numerical method and the computational program was justified by comparing the present CFD results of the fruit fly flapping motion in three modes, i.e., the advanced mode, the symmetrical mode and the delayed mode, with Dickinson＇s experimental results. They agreed with each other very well. Subsequently, the aerodynamic characteristics of the new bionic flapping motion in three modes were also numerically simulated, and were compared with those of the fruit fly flap- ping. The conclusions could be drawn that the high unsteady lift mechanism of the fruit fly hovering is also effectively utilized by this new bionic flapping. Compared with the fruit fly flapping, the unsteady drag of the new flapping decreases very much and the ratio of lift to drag increases greatly. And the great discrepancies among the mean lifts of three flapping modes of the fruit fly hovering are effectively smoothed in the new flapping. On the other hand, this new bionic flapping motion should be realized more easily. Finally, it must be pointed out that the above conclusions were just drawn for the hovering flapping motion. And the aerodynamic characteristics of the new bionic flapping motion in forward flight are going to be studied in the next step.

OSCILLATION PHENOMENA IN FAR FIELD REGION OF PLANE JETS AT LOW REYNOLDS NUMBERS

Oscillation phenomena in far field region of plane jets are studied by lattice Boltzmann method over a range of Reynolds numbers ( Re ) from 16to 65.Numerical results show that the instantaneous centerline velocities show periodic oscillation behavior in far field region when Re>38.In contrast , the periodic behavior is invisible in corresponding flow field when Re≤38.For the cases of Re≤38 , the exchange of momentum due to straining motion gradually dominates the downstream flow filed , which qualitatively suggests the possibility of jet instability.

Effects of relative thickness on aerodynamic characteristics of airfoil at a low Reynolds number

This study focuses on the characteristics of low Reynolds number flow around airfoil of high-altitude unmanned aerial vehicles（HAUAVs） cruising at low speed.Numerical simulation on the flows around several representative airfoils is carried out to investigate the low Reynolds number flow.The water tunnel model tests further validate the accuracy and effectiveness of the numerical method.Then the effects of the relative thickness of airfoil on aerodynamic performance are explored, using the above numerical method, by simulating flows around airfoils of different relative thicknesses（12%, 14%, 16%, 18%）, as well as different locations of the maximum relative thickness（x/c = 22%, 26%, 30%, 34%）, at a low Reynolds number of 5 × 10^5.Results show that performance of airfoils at low Reynolds number is mainly affected by the laminar separation bubble.On the premise of good stall characteristics, the value of maximum relative thickness should be as small as possible, and the location of the maximum relative thickness ought to be closer to the trailing edge to obtain fine airfoil performance.The numerical method is feasible for the simulation of low Reynolds number flow.The study can help to provide a basis for the design of low Reynolds number airfoil.

Aerodynamic Performance of the Locust Wing in Gliding Mode at Low Reynolds Number

Gliding is an important flight mode for insects because it saves energy during long distance flight without wing flapping. In this study, we investigated the influence of locust wing corrugation on the aerodynamic performance in gliding mode at low Reynolds number. Numerical simulations using two-dimensional Navier-Stokes equations are applied to study the gliding flight, which reveals the interaction between forewing and hindwing. The lift of the corrugated airfoil in a locust wing decreases from the wing root to the tip. Simulation results show that the pressure drags on the forewing and hindwing increase with an increase in wing thickness; while the lift-drag ratio of the airfoil is marginally affected by the corrugation on the airfoil. Geometric parameters analysis of the locust wing is also carried out, which includes the corrugation height, the corrugation placement and the shapes of leading and trailing edges.

Effects of surface roughness on the aerodynamic performance of a high subsonic compressor airfoil at low Reynolds number

The aerodynamic performance of compressor airfoil is significantly affected by the surface roughness at low Reynolds number(Re).In the present study,numerical simulations have been conducted to investigate the impact of surface roughness on the profile loss of a high subsonic compressor airfoil at Re=1.5×10^(5).Four roughness locations,covering 10%,30%,50%and 100%of the suction surface from the leading edge and seven roughness magnitudes(Ra)ranging from 52 to525 lm were selected.Results showed that the surface roughness mainly determined the loss generation process by influencing the structure of the Laminar Separation Bubble(LSB)and the turbulence level near the wall.For all the roughness locations,the variation trend for the profile loss with the roughness magnitude was similar.In the transitionally rough region,the negative displacement effect of the LSB was suppressed with the increase of roughness magnitude,leading to a maximum decrease of 14.6%,16.04%,16.45%and 10.20%in the profile loss at Ra=157 lm for the four roughness locations,respectively.However,with a further increase of the roughness magnitude in the fully rough region,the stronger turbulent dissipation enhanced the growth rate of the turbulent boundary layer and increased the profile loss instead.By comparison,the leading edge roughness played a dominant role in the boundary layer development and performance variation.To take fully advantage of the surface roughness reducing profile loss at low Re,the effects of roughness on suppressing LSB and inducing strong turbulent dissipation should be balanced effectively.

Study on effects of thickness on airfoil-stall at low Reynolds numbers by cusp-catastrophic model based on GA(W)-1 airfoil

The phenomena of an airfoil stall present the behaviors of catastrophe and hysteresis at low Reynolds numbers.Numerical simulation results of two-dimensional airfoil GA(W)-1 show that the width of the hysteresis loop of airfoil stall will gradually decrease and even disappear with the decrease of thickness ratio.These nonlinear characteristics are in accordance with the topological features of the cusp catastrophic model.According to the topological invariant principle,a novel topological mapping method is developed to establish the mapping relationship between cusp catastrophic model and stall characteristics of the airfoil,then the effect of thickness ratio on airfoil stall is successfully described quantitatively by cusp catastrophic model.Further,based on the established topological mapping relationship,combined with the mean flow field of the airfoil stall,potential function approach of cusp catastrophic model is first introduced to interpret the catastrophe and hysteresis of the airfoil stall,and it is found that as the thickness ratio decreases,the system’s maximal potential energy gradually disappears,and the short separation bubble at the leading edge of the airfoil changes to long separation bubble,so the airfoil stall changes from a bistable system to a monostable system.

Numerical study of separation on the trailing edge of a symmetrical airfoil at a low Reynolds number

This study focuses on the trailing-edge separation of a symmetrical airfoil at a low Rey-nolds number. Finite volume method is adopted to solve the unsteady Reynolds-averaged Navier-Stokes （RANS） equation. Flow of the symmetrical airfoil SD8020 at a low Reynolds number has been simulated. Laminar separation bubble in the flow field of the airfoil is observed and process of unsteady bubble burst and vortex shedding from airfoil surfaces is investigated. The time-dependent lift coefficient is characteristic of periodic fluctuations and the lift curve varies nonlinearly with the attack of angle. Laminar separation occurs on both surfaces of airfoil at small angles of attack. With the increase of angle of attack, laminar separation occurs and then reattaches near the trailing edge on the upper surface of airfoil, which forms laminar separation bubble. When the attack of angle reaches certain value, the laminar separation bubble is unstable and produces two kinds of large scale vortex, i.e. primary vortex and secondary vortex. The periodic processes that include secondary vortex production, motion of secondary vortex and vortex shedding cause fluctuation of the lift coefficient. The periodic time varies with attack of angle. The secondary vortex is relatively stronger than the primary vortex, which means its influence is relatively stronger than the primary vortex.

Spatio-temporal instability of two-layer liquid film at small Reynolds numbers

The onset of instability with respect to the spatio-temporally growing disturbance in a viscosity-stratified two-layer liquid film flow is analyzed. The known results obtained from the temporal theory of instability show that the flow is unstable in the limit of zero Reynolds numbers. The present theory predicts the neutral stability in the same limit. The discrepancy is explained. Based on the mechanical energy equation, a new mechanism of instability is found. The new mechanism is associated with the convective nature of the disturbance that is not Galilei invariant.

Effects of Bionic Leading Edge on the Aerodynamic Performance of a Compressor Cascade at a Low Reynolds Number

To achieve high-performance compressor cascades at low Reynolds number(Re),it is important to organize the boundary layer transition and separation processes efficiently and reasonably.In this study,the airfoil is focused on at a 5%blade height at the root of the orthogonal blade in the downflow passage of the high-load booster stage.The bionics modeling design is carried out for the leading edge of the original blade cascade;the response characteristics of laminar transition and separation to blades with different leading edge shapes at low Reynolds numbers are studied by using large eddy simulations combined with Omega vortex identification.The findings of this study demonstrate that bionic leading edge modeling can significantly improve the aerodynamic performance of blades at low Reynolds numbers.The blades effectively suppress the formation of separation bubbles at low Reynolds numbers and weaken or even eliminate large-scale flow separation at the trailing edge.In addition,the blades can weaken the vortex intensity on the blade surface,reduce the areas of high-velocity fluctuations,and minimize aerodynamic losses caused by turbulence dissipation.These results should serve as a valuable reference for the aerodynamic design and flow control of the high-load booster stage blade at low Re.

Mechanisms for non-ideal flow in low-power arc-heated supersonic nozzles

The flow in a low-powered arc gas heater com- bined with a supersonic nozzle of throat diameter less than 1 mm is quite complicated and difficult to describe in quan- titative detail. Experiments on arc-heated supersonic jet thrusters of monatomic gases argon and helium have been carried out and their performance measured. The flow charac- teristics are analyzed with the help of numerical simulation. Results show that the viscous effect is the most important factor causing the large difference between ideal and real performance. A large outer section of the exit flow is slow- moving. This is especially pronounced in helium, where 70 % of the exit area of the nozzle might be in subsonic flow. Fric- tion forces can be much larger than the net thrust, reaching several times higher in helium, resulting in very low efficien- cies. Other factors causing the differences between ideal and real flow include： complex flow in the throat region, electric arc extending to the nozzle expansion section, heat transfer to the inlet gas and from the hot plasma, and environmen- tal pressure in the vacuum chamber. It is recognized that the ordinary concepts of supersonic nozzle flow must be greatly modified when dealing with such complicated situations. The general concepts presented in this paper could be helpful in guiding the design and operation of this equipment.

Numerical Simulation of Stall Flow Control Using a DBD Plasma Actuator in Pulse Mode

A numerical simulation method is employed to investigate the effects of the unsteady plasma body force over the stalled NACA 0015 airfoil at low Reynolds number flow conditions. The plasma body force created by a dielectric barrier discharge actuator is modeled with a phenomenological method for plasma simulation coupled with the compressible Navier-Stokes equations. The governing equations are solved using an efficient implicit finitevolume method. The responses of the separated flow field to the effects of an unsteady body force in various inter- pulses and duty cycles as well as different locations and magnitudes are studied. It is shown that the duty cycle and inter-pulse are key parameters for flow separation control. Additionally, it is concluded that the body force is able to attach the flow and can affect boundary layer grow that Mach number 0.1 and Reynolds number of 45000.

THE THREE-DIMENSIONAL FUNDAMENTAL SOLUTION TO STOKES FLOW IN THE OBLATE SPHEROIDAL COORDINATES WITH APPLICATIONS TO MULTIPLES SPHEROID PROBLEMS

A new three-dimensional fundamental solution to the Stokes flow was proposed by transforming the solid harmonic functions in Lamb's solution into expressions in terms Of the oblate spheroidal coordinates. These fundamental solutions are advantageous in treating flows past an arbitrary number of arbitrarily positioned and oriented oblate spheroids. The least squares technique was adopted herein so that the convergence difficulties often encountered in solving three-dimensional problems were completely avoided. The examples demonstrate that present approach is highly accurate, consistently stable and computationally efficient. The oblate spheroid may be used to model a variety of particle shapes between a circular disk and a sphere. For the first time, the effect of various geometric factors on the forces and torques exerted on two oblate spheroids were systematically studied by using the proposed fundamental solutions. The generality of this approach was illustrated by two problems of three spheroids.

鞭毛/纤毛内在驱动机制启发的一体式管状机器人驱动器

鞭毛和纤毛独特的运动模式(如鞭毛的平面/螺旋波形式推进和纤毛的二维/三维不对称搏动)在众多生物的生命活动中起到至关重要的作用,这也启发了诸多仿生设计,尤其对于微型机器人系统。然而,与自然界中微生物能够从统一化的9+2轴丝生物结构中进化出多种运动模式不同的是,当前的仿生学仍然没有有效的工程策略去实现这样的智慧。在此,我们通过研究鞭毛和纤毛的内部结构及其内在驱动机制,推导出了一个统一的物理模型来描述微管弯曲及其所构建的宏观鞭毛/纤毛运动。基于该模型,我们进而提出了基于三通道的管状驱动概念,并相应地通过杆嵌入铸造工艺制造了一个三通道的管状驱动器。通过编程不同通道的驱动模式,这一管状驱动器不仅可以再现自然界中多样的二维及三维鞭毛/纤毛运动,还可以延展出更多的非对称纤毛搏动模式以实现低雷诺数下的有效推进。该研究加深了我们对微生物推进机制的理解,为仿生系统的设计提供了新灵感,并有望在广泛的工程领域中寻找到重要的应用场景。

Designing a Biomimetic Ornithopter Capable of Sustained and Controlled Flight

We describe the design of four ornithopters ranging in wing span from 10 cm to 40 cm, and in weight from 5 g to 45 g. The controllability and power supply are two major considerations, so we compare the efficiency and characteristics between different types of subsystems such as gearbox and tail shape. Our current omithopter is radio-controlled with inbuilt visual sensing and capable of takeoff and landing. We also concentrate on its wing efficiency based on design inspired by a real insect wing and consider that aspects of insect flight such as delayed stall and wake capture are essential at such small size. Most importantly, the advance ratio, controlled either by enlarging the wing beat amplitude or raising the wing beat frequency, is the most significant factor in an ornithopter which mimics an insect.

Analytical solution of the low Reynolds third-grade non-Newtonian fluids flow inside rough circular pipes

The present paper focuses on finding an analytical solution for fully developed third-grade non-Newtonian fluids flows inside rough circular pipes at low Reynolds numbers(Stokes flows).The wall roughness is modeled by two different periodic morphologies based on sinusoidal and triangular geometries.In this study,the relative roughness(ratio of the roughness amplitude to the pipe hydraulic diameter)is selected to be a small value,which is appropriate for the perturbation analysis.The governing parameters including the axial and radial velocity profiles,stream function,wall shear stress,pressure gradient,and friction factor are expressed in analytical formulas and they are compared to the smooth pipe.The effect of the relative roughness,the wall wave number,and the non-Newtonian parameter on the governing parameters are investigated.The results show that modeling the roughness by triangular geometry has a better prediction of pressure drop regarding the basic solution of the smooth pipe.

Speedup of self-propelled helical swimmers in a long cylindrical pipe

Pipe-like confinements are ubiquitously encountered by microswimmers.Here we systematically study the ratio of the speeds of a force-and torque-free microswimmer swimming in the center of a cylindrical pipe to its speed in an unbounded fluid(speed ratio).Inspired by E.coli,the model swimmer consists of a cylindrical head and a double-helical tail connected to the head by a rotating virtual motor.The numerical simulation shows that depending on swimmer geometry,confinements can enhance or hinder the swimming speed,which is verified by Reynolds number matched experiments.We further developed a reduced model.The model shows that the swimmer with a moderately long,slender head and a moderately long tail experiences the greatest speed enhancement,whereas the theoretical speed ratio has no upper limit.The properties of the virtual motor also affect the speed ratio,namely,the constant-frequency motor generates a greater speed ratio compared to the constant-torque motor.

Experimental Verification for the Application Feasibility of Buckingham Pi Theorem in Designing a Scaled Model of Flagellated Swimmer with Traditional Resistive Force Theory

The microstructure of bacterial is an important reference to design underwater swimmers. Applying Buckingham Pi Theorem is a possible method to build a scaled model based on a theoretical flagellum designed with traditional Resistive Force Theory. By making a scaled model, the forward velocity could be obtained to verify the application feasibility of Buckingham Pi Theorem in such designs. The optimal value of the model’s pitch angle can be calculated with the traditional RFT as well as the forward velocity. Comparing the experimental results with the results of theoretical calculations, it is found that the experimental and calculated results are consistent, which means Buckingham Pi Theorem works well in such design of underwater swimmer.